Question 389212: Rica A costs Php 20 per kilo and Rice B costs Php 25 per kilo. How many kilos of each kind must be mixed to produce a 30-kl mixture which costs Php 23 per kilo?
Answer by gwendolyn(128)   (Show Source):
You can put this solution on YOUR website! Let a be the amount of A (the Php 20/kilo kind) rice we will need.
Let b be the amount of B (the Php 25/kilo kind) rice we will need.
We know that the total amount will be 30 kilos. So, we can form an equation based on the amount of each rice and the total amount:
a kilos + b kilos = 30 kilos
Solving for a (or b, but we pick one at random):
a + b = 30
a + b - b = 30 - b
a = 30 - b
Our second equation will use the cost.
We know the cost per kilo of each rice and the amounts have been assigned variables (a, b). Multiplying each amount by its cost per kilo will tell us the the cost each type of rice contributes. We will total those to equal the combined cost (30 kilos at Php 23/kilo). So, in equation:
20 * a + 25 * b = 23 * 30
We now substitute out value of a in from the first equation:
20 * (30 - b) + 25b = 23 * 30
Distributing the 20 and doing the math:
600 - 20b + 25b = 690
600 + 5b = 690
600 + 5b - 600 = 690 - 600
5b = 90
5b/5 = 90/5
b = 18
Substituting into our first formula:
a = 30 - b
a = 30 - 18
a = 12
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